So I've been busy at uni for the last two weeks, hence no blog. I started back and then got hit by so much work, I've never had as much work as I do now. After two weeks I've been given three assignments, an been presented with a project which is meant to take me about 6 weeks to do. I'm doing 50 units this semester, and as a second year student, doing two third year courses and three second year courses. One of the first things that was said in one of the third year courses was "this course is harder then some honours courses..." which didn't sound fun. I'm also doing complex analysis which is a third year course, but that sounds fun. I'm doing a computational mathematics course as well which seems fun so far. Me and another person have done a bit of programming before and the teacher didn't mind helping us out with some more advanced stuff in our tutes which is cool. I'll get to it later though. I'm doing linear algebra as well and the lecturer is pretty funny, I had a chat with him when I was walking out of one of my tutes and he said that I'd enjoy a talk by Wadim Zudilin on the Zeta Function which is described as the most important function in all of matheamtics.
At that talk, I was talking to Jon Borwein, who I'd like to do a PhD under one day, and I didn't realise it was him at first becasue I've never spoken to him before and I was asking stuff about being accessible and then he commented about not knowing who I was and then I felt like an idiot. Jon Borwein is a world reknown expert on the mathematical constant pi by the way.
As for the Collatz Project part of this blog. For my project for the computational mathematics course, I'm intending to do something on the Collatz Conjecture which is a recursive function, and it is conjectured that no matter which number you start with (provided its a positive integer) then if you put the number into the function enough times, you'll always end up at the number 1. The function is defined as f(n)=n/2 if n is even, and f(n)=3n+1 if n is odd. Take the number 5, f(5)=16 because 5 is odd so you have to multiple it by 3 and add 1 to it, then you feed 16 to the function, so f(16)=8 because its even and you need to divide an even number by 2. This will continue until you get to 1. If you count the number of times you have to put a number into the function before you reach one, then plot it all, then you'll end up with a graph that has two very distinct looking sections in it, it looks like it is made up of a family of log curves and a family of exponential decay curves. There is an obvious(to a mathematically inclined person) a lower bound on the number of iterations required for a number, and that is log(n) and the bound is only touched when n satisfies 2n is an integer. Me and the person I was working with yesterday gave an upper bound as well, but it was only linear (a straight line) and the worst we can tell the bound should be is a log curve. We also placed a few of log curves through the point which has coordinates (27,111) where 27 is the number inputted at first to the function f, and the 111 is the number of iterations taken to reach 1. Note that 27 is an outlier of the neighbourhood it is in, the numbers 26 and 28 take far less then 111 iterations to reach 1. This curve we plotted will only go through 27, 54, 108,.... But we can plot an infinite number of these curves and get it to go through all the points if we needed I believe.
My lecturer for the computer course wrote a prime number sieve which I thought he was writing inefficeintly, but it turns out I was greatly unawares of what he was actually doing. It was genius! Much better then any of my implentations of the same sieve.
I'm also downloading an iso for a linux OS at the moment, which is almost 2GB in size, and the site I'm taking it from is only allowing me to download at about 83kB/s which means its taken almost 7hrs to downloa:( at least it will when its done. On the plus side, there is only 5 releases of it so I don't think they are going to update it any time soon which is good. Maybe I should've downloaded it at the uni. Its only halfway done now. I'm going to try and make a persistent USB version of it which I can then use almost anywhere. If I really like it I might put it on my laptop and just do away with Vista entirely because it drains my battery too fast (from fully charged it takes about 30 minutes before it starts not liking the level left in the battery). Hopefully my blog is not so popular that it will slow down my download.
Also when I get the chance, I think I'm going to make comments for blog. I just need to be bothered to adjust everything.
Oh and I've gotten more then 100 downloads of my app! Anyone who has a dvd/video game/book and an Android phone/tab should download it! It will get an update to make it easier to add stuff to it when I get the time! It will also get ads eventually too.
Latest updates to the site:
- Added a "Mathematics "papers"" section
- Added details to my personal IRC server
- Added a twitter widget on the home page
- Have some images and QRcode for the Media Manager app
- Added the Media Manager app
- Added a link to android apps
- Added a "Latest Blog" section on the home page
- The blog has been set up and blog entries have been made
- The site has been rearranged and now looks better